If you are tracking an injured bear, chances are you will be within 30-40 feet to make the kill.Disagree on that last part.
Any pistol cartridge has the potential to kill a bear. But some are much better suited for such a task than others.
I too have heard the story of the Alaskan guide who took down a grizzly with 9mm. I know that it can be done; that doesn't mean it should be done. You're taking a lot more risk with a smaller cartridge like that, which carries less energy compared to the 3 mentioned above. 9mm, and the other usual considerations for everyday carry (.40s&w and .45 acp) are out of the question for my purposes. I need a bit more certainty from whatever handgun I'm carrying; those lighter cartridges just don't provide that.
The deer and bear trackers I've talked all seem to lean towards .357 magnum or heavier magnums (and revolver platforms). I haven't heard of anyone carrying 10mm, though I'm sure with the appropriate ammo it will offer similar performance to that of .357 mag.
A 22LR with the proper gun and placement will kill the bear with 1 shot, 100% of the time.
Like @Willjr75 is saying, a 9mm has enough "power" to hit blood carrying vitals, which is how pistols kill things.
So, enough is enough, the bear will not be more dead just because the bullet hit vitals faster.